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This homework will define and, hopefully help you understand,
some of the basic notation involved with manipulating strings.

Given the alphabet Σ = {a,b,c}, what is the language of all
strings that start and end in c, with length at most three.
[Remember: a language is by defintion a set!]

Concatenation of strings, i.e. gluing strings
together, is indicated by placing strings next to one another.
so if w = abb and x = ba, then wx = abbba.
 Let x = bba, y =
aab, and z = bcb. What is yxz?
 For strings u and v, is it always true that
(uv)^{R} = vu?
Convince me of your answer! ["R" means reverse a string.
So (abb)^{R} = bba.]

We denote the length of a string w as w ... like magnitude
for a vector.
For strings u and v, what can you say about uv?

Consider the mystery string λ. Suppose that for any string
w, we have wλ = w. What can you tell me about
λ?

We often represent the characters in a string like this:
w = a_{1}a_{2}...a_{k}.
Suppose I define the "George" of a string
w = a_{1}a_{2}...a_{k}
to be a_{2}a_{1}
a_{4}a_{3}
...
a_{k}a_{k1}.
 What is the "George" of abcccb?
 What is the "George" of λ from the previous problem?
 Is there any string for which the "George" as I've
described it is not unambigiously defined? Explain!
Note: do not give "λ" as your answer!